Osnovy teorii Galua.

~1. Koneqibie floAR 157 5, By~eM Ha3bJBaTb H enpHHB 01AH M blM IT10 M OJ YJIJO p nIOAHHOM f (x) c pB[lx4OHaVlbHWMH KOB ~dHatHeHTamn ToraJa, eCJH er-0 HeJ~b3S1 npeazCTaeHmh B eii~e f (X)=g(x) h (x) +p px) rae g (x), h (x), cp (x) nIoJHHOMbl c qeaJb1mHi p.U~HOHaJlbHb1MH Ko34)4)H1uiieHTaMH. B flP0TH BHOM caiyqae 6yaeM TaKM( roBlOpHTb, 4T0 f (X) a A H T C H Ha g (x) 11 om0oa ynIto p. TomriiaIMeeT meCTO T eop e Ma 82. BCKaff BeJ114414HIa KOHeqHoro 1101114, yA~oBJeTBop5HIOtuaaf Hen1pHB0U4KM0My no m01Ly111 p ypaBHeHtito n-ft CTeneni-i c paIUH0 -HaJlbHbIM H KOcjx~HLLmeHTamH, yJLOBaTeTopnue Mm}K ) paBHeHH10 xpn _x- 0 Jo K a 3 a Te A1 b C T B3 0. FHyCTb a icopeHb HenpHBOAh1moo no0 molaymIo p ypaBHeHHSH f (x) z-0. Tortaa C0BOKyflfH0CTb BeJ1HliHlH ao + alm + a2a 2 f... + + On__ a"-, ri~e BeJi144HHbl a0, all,..., a.-1 rpo6eralOT He3BB11Ctim0 upyr OT Apyra 3HaqeHH14. (1.2), COCTaBlT -no~ne nopjima pt'. B camom ae~ne, 9TH1 BeaJiH4HHbl pa3uIHrnwb, TaK Ka i B HlPOT14BR0M cuiyqae BejIIII4Ha a yuloBJIeTBOpnlria 6h1 ypaBue~lio CTe11eHH <ft. IlYCTb g (X) = 0 6yie, ypaB~e~iie camofl HH3K0R CTeIneHH, KOTOPOMY YJtOBjieTB0O14eT a. Torma, aeasi f (x) Hagx) Mbl 110JYtIHM B OCTaTKe 11ojH4HMo eae 6o.'iee H143KOAI CTeIneHH, KOTOrOMY 6yuaeT yJa0Bj1eTBOPS1Tb a, H B CHJ1Y Hauwelo YCJ10BHI OTHOCHTeJ~bHO g(X) OHi AO1JI}KeH 6bITb To)KLaeCTBeHH-O pa~ell HYJItO, T. e. ero K03cl~clI4Lme[HTbl, paccmaTpHBaemble, KaK 9J1emeHTbl KOHeqH~or 110111, JLOJDKH<H 6bTEm PaBHbl Hy.10I. Pac. cmaTPHBaemb1e wKe, KaiK 06b11(HOBeHHbie 'IHcua, OHH AWOJI~HbI ALeJ1HTbCfl Ha p. OTCio0aa mbi Bony4HM paBeHCTBO BH~a f (x) =g (x) h(x) +p.(x), 'ITO ITPOTHBopeMHT HeCHPIBOJLHMOCTH nOJ11H~oma f (x) no moaynJ1o p. 14TOOE1 lLOKa3aTh, 'ITO BeJ1iqHHb1 ao + a~a +.... + a,-, anil o6paayior no~ne, caieayeT y6eaHTbCff, 'TO 01-11 YJOBJ1TBOP5l1or aKC~iomam I -IV (r~qaea LI, ~ 3.1). 3iecb e114HCTBeHHoe 3aTpyJ1HeHHi Mtow1eT npe1RCTaBHT'f.goKa3aTe.'IhCTBO Toro, WIO Bce 9TH BeJII4liHHb1, Kp0Me HyJI1, o6pa3ylor rpyniiy OTH1OCHTeJnbHO ymHowefHH14 (cytateTBoBauHie o6paTHoLo gJIemeHTa). nlyCmb Tpe6yeTC~l MAHaT1 BeHi'i1-IMy, o6paTHY1o K (p(x), rite T,(x) ITOMIHOM CTeflCHH HH>Ke n. Haflaem, rnoJb3y~lCb aIJIrOptiTMOM Z)BK~iHJa, O6uttift Hati6011bWu14 11eJ114TeJb I? nHOJIHOMOB f1(X) Hi cp (x). Tori~a nmeeT meCTO T02KAeCTBO rite g (x) ii h (x) - HOJlHHOlMbl C LieIab1mi pam4LHOHJqbHb1Mll K03(1)4)HLHeHTamH (CM. riany II, ~ 4). Hlpf 9TOm TlpexionoJtiOm, 'ITO XOT b '0111-H 1-3 K094)C()H-,[LHeHTOB nOHOJHOMOB g(X), h (x) He JJemITC5I Ha p. Ecuu 6bi R aenllA0oCb Ha p, To0 B Cilyqae, ecJ1H He BCe K0344(~HmmleTbI noJikIHma h (x) aLe!lIHTCII Ha p, Mb! 6bi U1OJlyqpiqiJ- nocue HoIICTatiOBKHl x a= B (1.5) paBei-CTBO p+ (a.).h (a) = 0, 'qTo nporHBope'I1411 6b1 HefHP14BO1UHMOCT1H f (X), TaK KaIK o6a, nOJIHHoma cp(x), h (X) Hme1OT c1Ce1eHb <nt. ECJIH we BCe K094)aPHLL~eHTbl

/ 232
Pages

Actions

file_download Download Options Download this page PDF - Pages 157-176 Image - Page 157 Plain Text - Page 157

About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page 157
Publication
Leningrad,: Gos. tekhniko-teoreticheskoe izd-vo,
1934-
Subject terms
Galois theory

Technical Details

Link to this Item
https://name.umdl.umich.edu/acr5415.0001.001
Link to this scan
https://quod.lib.umich.edu/u/umhistmath/acr5415.0001.001/161

Rights and Permissions

The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].

DPLA Rights Statement: No Copyright - United States

Manifest
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:acr5415.0001.001

Cite this Item

Full citation
"Osnovy teorii Galua." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/acr5415.0001.001. University of Michigan Library Digital Collections. Accessed April 30, 2025.
Do you have questions about this content? Need to report a problem? Please contact us.